The present investigation is concerned with a class of slip-line field solutions for metal machining involving chip curl. The solutions under consideration were first proposed by Kudo, who had found them to be statically inadmissible. In this study, these fields are analysed by assuming an elastic contact zone beyond the plastically stressed region. Force and moment equilibrium of the chip is realised by assuming the rigid chip to be acted upon by prescribed normal and shear forces in the elastic zone and by forces in the rigid–plastic boundary. Results are presented for variation in contact length, cutting force and thrust force, with variation in rake angle and interface friction conditions, both for power-law and exponential pressure distributions in the elastic contact zone.